Comments for MEDB 5501, Week 8

Review two-sample t-test

  • \(H_0:\ \mu_1=\mu_2\)
  • \(H_1:\ \mu_1 \ne \mu_2\)
    • Or a one tailed alternative
  • \(T=\frac{\bar X_1-\bar X_2}{SE(\bar X_1-\bar X_2)}\)
    • Accept H0 if T is close to zero.

What to do with three or more groups?

  • \(H_0:\ \mu_1=\mu_2=...=\mu_k\)
  • \(H_1:\ \mu_i \ne \mu_j\) for some i, j
    • Note: one-tailed test is tricky.
  • Accept H0 if the F ratio (defined below) is close to 1.

Artificial data

   g  y
1  1 23
2  1 30
3  1 25
4  2 33
5  2 36
6  2 41
7  2 37
8  2 43
9  3 24
10 3 29
11 3 31

Scatterplot

Total SS = 452

Within SS = 116

Between SS = 336

Degrees of freedom

  • For Total SS, df = 10
  • For Within SS, df = 8
  • For Between SS, df = 2
  • In general,
    • N = number of observations
    • k = number of groups
      • Total df = N-1
      • Within df = N-k
      • Between df = k-1

ANOVA table, 1 of 4

ANOVA table, 2 of 4

ANOVA table, 3 of 4

ANOVA table, 4 of 4

ANOVA table from the general linear model

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis

YRBSS analysis